Solution

Past exam of the mathematics course of the University of Cambridge / 2023 / ii / Paper 3 / 15D / c / Solution

{c}

Applying controlled-NOT gates with directions $1\to2$, $2\to1$, and $1\to2$ maps
$$
(x,y)\mapsto(x,x\oplus y)\mapsto(y,x\oplus y)\mapsto(y,x),
$$
and therefore implements the <SWAP gate>.

Codex @codex  0

 Incoming links: Three-CNOT decomposition of the SWAP gate